More on the dynamics of the symbolic square root map

نویسندگان

  • Jarkko Peltomäki
  • Markus A. Whiteland
چکیده

In our earlier paper [A square root map on Sturmian words, Electron. J. Combin. 24.1 (2017)], we introduced a symbolic square root map. Every optimal squareful infinite word s contains exactly six minimal squares and can be written as a product of these squares: s = X2 1X 2 2 · · · . The square root √ s of s is the infinite word X1X2 · · · obtained by deleting half of each square. We proved that the square root map preserves the languages of Sturmian words (which are optimal squareful words). The dynamics of the square root map on a Sturmian subshift are well understood. In our earlier work, we introduced another type of subshift of optimal squareful words which together with the square root map form a dynamical system. In this paper, we study these dynamical systems in more detail and compare their properties to the Sturmian case. The main results are characterizations of periodic points and the limit set. The results show that while there is some similarity it is possible for the square root map to exhibit quite different behavior compared to the Sturmian case.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A New Approach to Detect Congestive Heart Failure Using Symbolic Dynamics Analysis of Electrocardiogram Signal

The aim of this study is to show that the measures derived from Electrocardiogram (ECG) signals many a time perform better than the same measures obtained from heart rate (HR) signals. A comparison was made to investigate how far the nonlinear symbolic dynamics approach helps to characterize the nonlinear properties of ECG signals and HR signals, and thereby discriminate between normal and cong...

متن کامل

A New Approach to Detect Congestive Heart Failure Using Symbolic Dynamics Analysis of Electrocardiogram Signal

The aim of this study is to show that the measures derived from Electrocardiogram (ECG) signals many a time perform better than the same measures obtained from heart rate (HR) signals. A comparison was made to investigate how far the nonlinear symbolic dynamics approach helps to characterize the nonlinear properties of ECG signals and HR signals, and thereby discriminate between normal and cong...

متن کامل

Molecular Docking Based on Virtual Screening, Molecular Dynamics and Atoms in Molecules Studies to Identify the Potential Human Epidermal Receptor 2 Intracellular Domain Inhibitors

Human epidermal growth factor receptor 2 (HER2) is a member of the epidermal growth factor receptor family having tyrosine kinase activity. Overexpression of HER2 usually causes malignant transformation of cells and is responsible for the breast cancer. In this work, the virtual screening, molecular docking, quantum mechanics and molecular dynamics methods were employed to study protein–ligand ...

متن کامل

Molecular Dynamics and Molecular Docking Studies on the Interaction between Four Tetrahydroxy Derivatives of Polyphenyls and Beta Amyloid

Interactions of 3,3',4,4'-tetrahydroxybiphenyl (BPT) and three isomeric 3,3",4,4"-tetrahydroxyterphenyls (OTT, MTT, PTT) with Alzheimer’s amyloid-β peptide (Aβ) were studied by molecular dynamics simulation and molecular docking. Structural parameters such as Root-mean-square derivations (RMSD), radial distribution function (RDF), helix percentage and other physical parameters were obtained. Th...

متن کامل

The Square of a Map, Symbolic Dynamics, and the Conley Index

We consider a map f from a locally compact metric space to itself, and use the discrete Conley index to study the difference between the local dynamics of f and f. In particular, we present a method, based on work by Mischaikow, Szymczak, et al., for detecting positive entropy symbolic dynamics by measuring the difference between Conley indices for f and f.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2017